To find Matthew's average mark for all the exams, we can follow these steps:
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Let the total marks in physics, chemistry, and biology be represented as \( T_1 \). Since his average mark in these three subjects is \( x \), we can express \( T_1 \) as: \[ T_1 = 3x \] (because there are three subjects).
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Let the total marks in history and geography be represented as \( T_2 \). Since the average mark in these two subjects is \( y \), we can express \( T_2 \) as: \[ T_2 = 2y \] (because there are two subjects).
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The total marks for all the subjects (which includes physics, chemistry, biology, history, and geography) will then be: \[ T_{\text{total}} = T_1 + T_2 = 3x + 2y \]
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The total number of subjects is \( 3 + 2 = 5 \).
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Now, we can find the overall average mark by dividing the total marks by the total number of subjects: \[ \text{Average mark} = \frac{T_{\text{total}}}{\text{Number of subjects}} = \frac{3x + 2y}{5} \]
Thus, Matthew's average mark for all the exams is: \[ \frac{3x + 2y}{5} \]
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